Lectures related to Calcul de valeurs propres

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Symmetric Matrices: Diagonalizability and Eigenvectors

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Diagonalization in Symmetric Matrices

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Diagonalization of Matrices

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Symmetric Matrices and Orthogonal Matrices

Covers the properties of symmetric matrices, orthogonal matrices, and eigenvalues.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Convergence Rate Theorem: Part 1

Delves into the proof of the convergence rate theorem for an ergodic Markov chain, emphasizing eigenvalues and detailed balance properties.

Symmetric Matrices and Eigenvectors

Covers the concept of symmetric matrices, orthogonal bases, and eigenvectors.

Symmetric Matrices: Eigenvalues and Eigenvectors

Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.